Turf War - Capture a Tactical Spawn Point 
Capture a Tactical Spawn Point for the first time
Tactical Spawn Points can only be captured while playing as the Tactician. On screen, they will be displayed as icons like this and appear as spotlights as shown below. To capture a Spawn Point, simply stand/crouch within its radius until the bar on-screen turns completely green. Some Spawn Points will provide you with access to Jet Packs and Exos on certain maps.
Spawn Point Icon:
Spawn Point Object:
Pilot's Wings - Mid-air kill 

Got a mid-air kill using the Jet Pack in any multiplayer mode
You must play on the Turbine Concourse SE-6 map in Warzone game mode in order to acquire this trophy. Jet Packs are located on each side of the map for both the ISA and Helghast and at Tactical Spawn Areas. You’ll find them folded up inside of what looks like a rack. Approach the equipment and press the

button to grab it. To activate it, press and hold

.
Press

to launch yourself into the air. While airborne you can press the

button to dash forward. This is especially useful to avoid enemy fire or to try and reach ledges/platforms otherwise out of your reach. Pressing

fires your machine gun. Take care not to fire it for too long or you’ll overheat your weapon thus leaving you vulnerable. You must be airborne (ie; not touching the ground) in order for the kill to count.
Video by
PowerPyx with ingame Map Location for Jetpack at the Tactical Spawn
Iron Man - Get a kill with the Exo 

Killed a player using the Exo in any multiplayer mode
The Exo is found only on the Corinth Highway map in Warzone game mode. There are 2 of these, 1 on each faction’s base for the ISA and Helghast. This devastating piece of equipment is very lethal, particularly in the hands of a skilled player. The armor can hold up to a modest amount of abuse and the weapons (Machine Gun & Rocket Launcher) are extremely accurate. Again,

is for the Machinegun, and

are the Rocket Launchers. Although the Exo provides you with some decent protection, be aware that you can still be killed very quickly by headshots and explosives
Video by
PowerPyx with Ingame Map Location of Exo at Helghast base
Grand Slam - Win a match in 3 multiplayer modes 
Won a match in Operation, Warzone & Guerilla Warfare modes
Win at least once in each of the 3 match types available: Operation, Warzone & Guerilla Warfare to unlock this. This can be done in separate sessions and does not need to be completed in one go.
Guerilla Warfare - Also known as Bodycount for Killzone veterans, this is a Team Deathmatch game where the first team to fill their kill quota wins.
Warzone - This is a best-of-7-rounds game that consists of 4 Sub-Missions: Search & Destroy (2 rounds), Assassination (2 rounds), Capture & Hold, Search & Retrieve and Bodycount. To win, your team must successfully complete the objective in at least 4 rounds.
Operation - One team will play as the Helghast defending a set of objectives and the other team will play as the ISA whose target is to blow up the objectives, and the teams will rotate once each map. The team that successfully attacks/defends their objectives at the end of the game wins.